Oddities of the Universe

Transcription

1 Oddities of the Universe Koushik Dutta Theory Division, Saha Institute Physics Department, IISER, Kolkata 4th November,

2 Outline - Basics of General Relativity - Expanding FRW Universe - Problems with FRW Universe - Inflation and its implications - Where we stand.. 2

3 Which way the train will go?

4 Einstein: Along the train line (1915) General Theory of Relativity

5 General Theory of relativity A New Theory of Gravity Matter causes space-time to stretch/bend/wrap Gravity: Responding to curvature of space-time Gravitational force (Newtonian) is replaced by the response to the curvature

6 A MODERN VIEW Curved spacetime is the background on which other things happen! Theatre stage :) Theatre stage changes as the actors in the stage change/move!

7 A MODERN VIEW Curved spacetime is the background on which other things happen! Theatre stage :) Theatre stage changes as the actors in the stage change/move! ds 2 = µ dx µ dx = dt 2 + ~ dx 2 Special Theory of Relativity

8 A MODERN VIEW Curved spacetime is the background on which other things happen! Theatre stage :) Theatre stage changes as the actors in the stage change/move! ds 2 = µ dx µ dx = dt 2 + ~ dx 2 Special Theory of Relativity What is the metric for our Universe?

9 300,000 yrs before 2.7 K

10 HOW GALAXIES LOOK

11 Make an educated guess Homogenous and isotropic universe Friedmann-Robertson-Walker Universe ds 2 = dt 2 + a(t) ~ dx 2 d~x 2 = dr 2 1 kr 2 + r2 d 2 expansion parameter

12 Make an educated guess Homogenous and isotropic universe Friedmann-Robertson-Walker Universe ds 2 = dt 2 + a(t) ~ dx 2 d~x 2 = dr 2 1 kr 2 + r2 d 2 expansion parameter Ideal fluid T µ =(,p,p,p) Eqn of state: p = w

13 Basic Equations

14 Basic Equations Hubble Constant Energy Conservation: / 1 a 3(1+w) Matter: w = 0 Radiation: w = 1/3 Cosmological constant: w = -1

15 Basic Equations p< (1/3) Accelerating Universe p = a(t) / e Ht a(t) / t n matter/radiation n<1

16 BBN 16

17 Content of the Universe Baryons: 4% Dark matter: 23% Unknown: 73% Massive neutrinos: 0.1% Spatial curvature: very close to 0 17

18 We know evolution We know content What else?

19 We know evolution We know content What else? Some fundamental problems in this picture! Oddities of the Universe

20 Old problem I k = k (ah) 2 =1 tot =1 X i i / crit crit =3H 2 o M 2 Pl Comoving Hubble radius 1 ah = 1 H 0 a (3w+1)/2 Curvature density grows for w > -1/3 Flatness problem

21 Old problem I Possibilities: (i) k = 0 to start with (ii) Initially fine tuned.. (iii) Dynamical mechanism: w < -1/3 INFLATION ä>0

22 Flatness problem: Inflation 1 Tot = k (ah) 2 Log inflation today time end of inflation 22

23 PLANCK 2015 T/T 10 5 Fluctuations ~ Homogenous and isotropic 23

24 Old problem II Comoving distance ( 1, 2 )= Z 2 i d =.. = 1 (ah) 2 2 3w +1 a/a f ) 3w Particle Horizon ( 1, ) = 1 ah = 1 2 3w +1 w > - 1/3 w < - 1/3

25 (Particle) Horizon Problem Comoving distance ( 1, 2 )= Z 2 i d =.. = 1 (ah) 2 2 3w +1 a/a f ) 3w Particle Horizon ( 1, ) = 1 ah = 1 z 2 3w +1 w > - 1/3 w < - 1/3 z Particle Horizon size Particle Horizon size (z) ph(z) ' 2p 1+z

26 0 Old problem II conformal time CMB sky Big bang singularity =0 (Particle) Horizon Problem 26

27 conformal time 0 Inflation CMB sky reheating =0 Inflation Big bang singularity 27

28 New problem coherent super-hubble perturbations l hubble 70 D TE l hq T lmq E lmi 150 T, = ACos(wt + )e i~ k = With random phase uniformly distributed DTE l =0 phase is not random 28

29 Inflation Additionally, primordial spectrum is scale invariant hr(~x 1 )..R(~x n )i = hr( ~x 1 )..R( ~x n )i de-sitter space-time ds 2 = dt 2 + e Ht dx 2 = d 2 + dx 2 2 H 2!, ~x! ~x d dt ((ah) 1 ) < 0 ä>0 29

30 Novelties ev scale measurements to probe 10^12 GeV Physics of GR + QFT Probing new energy scales/new physics (i) E 1 H (ii) E 2 /E 1 Ḣ/H2 (iii) E 3 Ḧ

31 log(1/ah) matter Inflation radiation reheating log(a) end of today inflation 31

32 INFLATION 101 p = V ( ) ' V ( ) = V ( ) ' V ( ) Minimal gravity & Canonical scalar field with V ( ) Slow-roll parameters: = M 2 pl(v 0 /V ) 2 = M 2 pl(v 00 /V )

33 0-th Order Inflation Friedmann Equation H 2 = 1 3 V ( ) Klein Gordon equation +3H = V 00 ( ) a(t) e H inf t Scale of inflation: H inf constant

34 PLANCK 2015 T/T 10 5 Fluctuations ~ Homegneous and isotropic 34

35 HOW GALAXIES LOOK

36 DENSITY PERTURBATIONS +3H = V ( ) H 2 = 1 3 (V ( ) )

37 DENSITY PERTURBATIONS +3H = V ( ) = X ke ikx H 2 = 1 3 (V ( ) ) k 2 H 2 inf Ak n s 1 A s V 3/2 V 0 A s =

38 Coherent sum of waves V K Comoving scale log(1/ah) matter Inflation radiation reheating N K log(a) CMB scales exit end of inflation today 38

39 issue of gauge choice etc.. GRAVITY WAVES R µ 1 A 2 t H 2 V 1/4 r 1/4 inf GeV Rg µ + g µ = 8 G c 4 T µ g µ r = A2 t A 2 s = O(1) M Pl r /2 Scalar spectral index: n s =1 6 +2

40 AWAY FROM SIMPLE.. features in the spectrum non-gaussianities Problem of too few observables non-adiabiticity

41 What is inflaton? Physics of inflation must be embedded with our knowledge of high energy physics? Find a suitable scalar field - Higgs/Moduli/ scalars in SUSY theory Why the potential remains flat? - Symmetry Can we embed inflation in more fundamental physics? e.g String theory How do you start inflation?

42 What inflation people do Several phenomenological models Predictions for statistical properties of CMB Model building in particle physics e.g SUGRA my research area.. Large field models of inflation - Chaotic inflation Small field models - Hybrid inflation Reference: TASI Lectures by Baumann arxiv.org:

43 Future.. EUCLID PRISM

44 CONCLUSIONS - Paradigm of inflation is well established: Solves outstanding problems of BB cosmology and explains the source of density perturbations! - Connection to particle physics is still better to be understood - Big question: Scale of inflation? - Detection of primordial gravity wave is crucial

45 Thank You